The Lyapunov theorem on convexity and its use for sign-embeddings

V. М. Kadets; М. М.  Popov

V. М. Kadets Kharkiv. Univ.
М. М. Popov Zaporizhzhia Univ.

Keywords: -

Abstract

It is proved (Theorem 1) that for a Banach space $X$ the following statements are equialent: i) the range of every $X$-valued $\sigma$-additive non-atomic measure of finite variation has convex closure; ii) $L_1$ does not sign-embed in $X$.

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